Hamiltonian formalism for two magnon scattering microwave relaxation: Theory and applications

Abstract

A two magnon scattering theory for microwave relaxation in magnetic systems is formulated in the framework of the Hamiltonian formalism. The paper provides general expressions for inhomogeneity coupling coefficients in the case of localized inhomogeneities. An approximate solution for the relaxation rate of the ferromagnetic resonance uniform mode relaxation rate is presented. Two examples of the application of the theory are presented, one for bulk polycrystalline ferrites and one for polycrystalline metallic thin films.

Tunable magnetization relaxation of Fe2Cr1−xCoxSi half-metallic Heusler alloys by band structure engineering

“…We calculated the magnon wave vector ( k 0 ) at which the spin wave energy degenerates with the uniform modes ω(k 0 ) = 2πf for a given propagation direction ϕ with respect to magnetization in the film plane [55,56]. The total contribution to TMS was then estimated using [57,58] : …”

Damping and modal structure of patterned magnetic nanoarrays

“…In this case, even if we do not know the details concerning the nonuniformities that cause the linewidth broadening, we can still use a simplified version of the timeindependent perturbation theory to roughly distinguish between broadening arising from nonuniformities and true damping [8,9]. De facto, we will refer to the first-order perturbation theory as ''inhomogeneous broadening'' while the second-order contribution will be called ''two-magnon scattering''.…”

Crystallographic anisotropy of the intrinsic Gilbert damping for single-crystalline Fe film

“…In ferromagnetic materials, the strength of the spin-orbit interaction is responsible for both the static and dynamic properties of magnetization, for example, a crystalline magnetic anisotropy and magnetization damping. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] Thus, similar to the crystalline magnetic anisotropy, one can expect that the Gilbert damping constant governing the magnetization damping will also show a crystallographic anisotropy. However, it is still unclear whether the Gilbert damping constant has crystallographic anisotropy.…”

“…[12][13][14][15][16][17][18][19] The linewidth is, however, not simply in proportion to the intrinsic Gilbert damping constant because extrinsic contributions such as two mangnon scattering (TMS) and inhomogeneous line-broadening (ILB) also increase the FMR linewidth. 11,16) To evaluate the intrinsic Gilbert damping constant precisely, those extrinsic contributions must be excluded. The out-of-plane angular dependence of the linewidth is typically measured to extract the intrinsic Gilbert damping constant from the FMR spectrum data.…”

“…Various theoretical approaches have been proposed to describe the anisotropy of the Gilbert damping term in the Landau-Lifshitz-Gilbert equation, which describes the precessional motion of magnetization. 1,[4][5][6][7][8][9][10][11] There are two types of anisotropy of α, a rotational anisotropy and an orientational anisotropy. The former is due to the change in damping for different directions of the temporal change in magnetization dM dt , and the latter is attributed to the damping dependence on the momentary orientation of M(t).…”